The Smog Monster is good but not My favorite one. Megaguirus is actually pretty good. It's the second movie out of the Millennium Series and it came out in 2000. Godzilla 1999/Godzilla Millenium/Godzilla 2000 was before this before was another reboot.
I didn't know if you and your son knew about Gamera. Did you post that trailer because you knew about it or is that because of your son knowing about Gamera I like him as much as I do Godzilla and his movies are quite good but I have always found some parts disturbing and I still do to this day. i don't know how it would affect a child from this era however though suppose if you can watch that gruesome fight with Mechagodzilla & Anguirus and not budge, cringe or feel anything at all then I suppose it wouldn't be that different here. There's usually children involved in the movies as Gamera is actually good and cares for kids in his monstrous way. I have always thought his enemy Kaijus were quite strange but very fun. My Mom recorded many of them for Me. There's not as many Gamera films as there is Godzilla.
That movie you posted is Gamera: Guardian of the Universe. This was the first of a trilogy in the reboot series. Their quite awesome and gave Toho's Heisei series a huge run for their money
Here's the very first Gammera/Gamera movie that came out in 1965 called Gammera The Invincible. He's a giant prehistoric Turtle awaken from the ice. I have always found his roar very pitiful sounding. He's the only Kaiju in this film however. Here's the Japanese Trailer
This is the US Traler. The movie IMO is a epic as the first Godzilla